ARTICLE IN PRESS
Journal of Financial Markets 12 (2009) 391–417 www.elsevier.com/locate/finmar
Option strategies: Good deals and margin calls
Pedro Santa-Claraa,1, Alessio Sarettob,Ã
aUniversidade Nova de Lisboa and NBER, Rua Marqueˆs de Fronteira, 20, 1099-038 Lisboa, Portugal bThe Krannert School, Purdue University, West Lafayette, IN 47907-2056, USA
Available online 19 January 2009
Abstract
We provide evidence that trading frictions have an economically important impact on the execution and the profitability of option strategies that involve writing out-of-the-money put options. Margin requirements, in particular, limit the notional amount of capital that can be invested in the strategies and force investors to close down positions and realize losses. The economic effect of frictions is stronger when the investor seeks to write options more aggressively. Although margins are effective in reducing counterparty default risk, they also impose a friction that limits investors from supplying liquidity to the option market. r 2009 Elsevier B.V. All rights reserved.
JEL classification: G12; G13; G14
Keywords: Limits to arbitrage; Option strategies
Dear Customers,
As you no doubt are aware, the New York stock market dropped precipitously on Monday, October 27, 1997. That drop followed large declines on two previous days. This precipitous decline caused substantial losses in the funds’ positions, particularly the positions in puts on the Standard & Poor’s 500 Index. [...] The cumulation of these adverse developments led to the situation where, at the close of business on Monday, the funds were unable to meet minimum capital requirements for the maintenance of their margin accounts. [...] We have been working with our broker- dealers since Monday evening to try to meet the funds’ obligations in an orderly
ÃCorresponding author. Tel.: +1 765 496 7591. E-mail addresses: [email protected] (P. Santa-Clara), [email protected] (A. Saretto). 1On leave from UCLA. Tel.: +351 21 382 2706.
1386-4181/$ - see front matter r 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.finmar.2009.01.002 ARTICLE IN PRESS 392 P. Santa-Clara, A. Saretto / Journal of Financial Markets 12 (2009) 391–417
fashion. However, right now the indications are that the entire equity positions in the funds has been wiped out. Sadly, it would appear that if it had been possible to delay liquidating most of the funds’ accounts for one more day, a liquidation could have been avoided. Nevertheless, we cannot deal with ‘‘would have been.’’ We took risks. We were successful for a long time. This time we did not succeed, and I regret to say that all of us have suffered some very large losses. — Letter from Victor Niederhoffer to investors in his hedge funds. Jackwerth (2000), Coval and Shumway (2001), Bakshi and Kapadia (2003), Bondarenko (2003), Jones (2006),andDriessen and Maenhout (2007) find that strategies that involve writing put options on the S&P 500 index offer very high Sharpe ratios (‘‘good deals’’)— close to two on an annual basis for writing straddles and strangles.2 In the finance literature the debate over the relevance of those results in determining whether out-of-the- money (OTM) put options are or are not mis-priced is quite fervid. On one hand, the strategies’ returns are difficult to justify as remuneration for risk in the context of models with a representative investor and standard utility function.3 Even fairly general semi- parametric approaches such as those followed by Bondarenko (2003) and Jones (2006) or non-standard utility functions, such as in Driessen and Maenhout (2007), have little success in explaining the high returns. On the other hand, Benzoni et al. (2005) study an economy where very low mean reversion in the state variable leads investors to keep buying options for insurance purposes long after a market crash has occurred, therefore keeping high prices of put options. Bates (2007) propose to evaluate the historical option returns relative to those produced in simulation by commonly used option pricing models. They find no evidence of mis-pricing when using a stochastic volatility model with jumps. A third stream of the literature investigates the impact of demand pressure on option prices. Bollen and Whaley (2004) show that net buying pressure is positively related to changes in the implied volatility surface of index options. Garleanu et al. (2005) argue that the net demand of private investors affects the way market-makers price options. In their model, high prices are driven by market makers who charge a premium as compensation for the fact that they cannot completely hedge an unbalanced inventory. In summary, Garleanu et al. argue that demand pressure causes option prices to be higher than they would otherwise be in the presence of a more widespread group of liquidity providers. Indeed, prices are so high that trading strategies that involve providing liquidity to the market (such as writing options) appear to earn an exceptionally high returns. On one hand if put options are mis-priced, perhaps because their prices are bid up by demand pressure, the question of why such trading opportunities have not attracted the attention of sophisticated investors, who do not need to be completely hedged, is still un- answered and therefore deserves attention. On the other hand, if put options are not
2Similarly, Day and Lewis (1992), Christensen and Prabhala (1998), Jackwerth and Rubistein (1996), and Rosenberg and Engle (2002) find discrepancies between the empirical and the implicit distribution of the S&P 500 returns. 3A large set of studies concludes that option prices can be rationalized only by very large volatility and/or jump risk premia. See, for example, Bates (1996), Bakshi et al. (1997), Bates (2000), Chernov and Ghysels (2000), Buraschi and Jackwerth (2001), Benzoni (2002), Pan (2002), Chernov et al. (2003), Eraker et al. (2003), Jones (2003), Eraker (2004), Liu et al. (2005), Santa-Clara and Yan (2004), Benzoni et al. (2005), Xin and Tauchen (2005), and Broadie et al. (2006). Bates (2001) introduces heterogeneous preferences while Buraschi and Alexei (2006) consider heterogeneous beliefs. ARTICLE IN PRESS P. Santa-Clara, A. Saretto / Journal of Financial Markets 12 (2009) 391–417 393 mis-priced and the high put option returns are due to very large premia for volatility and/ or jump risk, a question still remains as to the ability of investors participating in the market. We do not attempt to distinguish between those two alternatives, but simply try to measure the impact of margins on the realized return of option trading strategies. In the broad sense, our paper therefore is focused on developing and testing the hypothesis that margin requirements, although effective in reducing counterparty default risk, impose a friction that might significantly blunt the effectiveness of option markets for risk sharing among investors. Margin requirements limit the notional amount of capital that can be invested in the strategies and force investors out of trades at the worst possible times (precisely when they are losing the most money). Our evidence indicates that, once margins are taken into account, the profitability and the risk-return trade off of the ‘‘good deals’’ is not as economically significant as previously documented. Therefore, we argue that these frictions make it difficult for investors (non-market-makers) to systematically write options. Our study analyzes data on S&P 500 options from January of 1985 to April of 2006, a period that encompasses a variety of market conditions. We study the effect of two different margining systems: the system applied by the Chicago Board of Options Exchange (CBOE) to generic customer accounts, and the system applied by the Chicago Mercantile Exchange (CME) to members’ proprietary accounts and large institutional investors. We find that the requirements imposed by the CBOE are more onerous and difficult to maintain than the requirements imposed by the CME. In both cases, margins affect the execution and the profitability of option strategies. In particular, margins influence the strategies along two dimensions: they limit the number of contracts that an investor can write, and they force the investor to close down positions. For example, a CBOE customer with an availability of capital equivalent to one S&P 500 futures contract could write only one ATM near-maturity put contract if she wanted to meet the maximum margin call in the sample. If the investor chose to write more contracts, she would not be able to always meet the minimum requirements. As a consequence, her option positions would have to be closed. Forced liquidations happen precisely when the strategies are losing the most money, or in other words when the market is sharply moving against the investor’s positions— a sudden decrease of the underlying value or an increase in market volatility. Therefore the investor is forced to realize losses. Partial and total liquidations due to margin calls also force the investor to execute a larger number of trades, increasing the importance of transaction costs. We test for the statistical relationship between the portfolio exposure to options and measures that proxy for the execution and the profitability of the strategies. The results of this analysis are supportive of our conjecture: increasing the portfolio exposure to the option and controlling for the level of coverage leads to a deterioration of the portfolio profitability and to a bigger difference between the effective and the target weight. We observe this positive relationship when we consider the Sharpe ratio, the Leland (1999) alpha, and the manipulation-proof performance measure (MPPM) of Ingersoll et al. (2007). In synthesis, the main result of this paper is that the difference between option ‘‘margined’’ realized returns and option ‘‘un-margined’’ returns can be quite substantial when investors are subject to margins and do not have unlimited access to capital when the market is in a downturn state. Consequently, our paper contributes to the literature that studies the impact of demand pressure on option prices by showing how frictions limit ARTICLE IN PRESS 394 P. Santa-Clara, A. Saretto / Journal of Financial Markets 12 (2009) 391–417 arbitrageurs from supplying liquidity to the market and hence releasing pressure on market-makers. In that sense, this study complements the results of Garleanu et al. (2005). Moreover, our results help explain the findings of Jones (2006). Jones considers returns before margins are taken into account and finds that only a portion of the returns can be explained by jump and volatility factors. We show that part of these ‘‘un-margined’’ returns are not available to investors and therefore should not be explainable in terms of remuneration for risk. Our paper also contributes to the vast literature that studies trading costs in option markets (see, for example, Constantinides et al., 2008) by offering evidence on the effect of a particular source of friction, which has not been explicitly considered: margin requirements.4 Consistent with the arguments of Shleifer and Vishny (1997), Duffie et al. (2002),and Liu and Longstaff (2004) about the limits to arbitrage, our findings could help explain why the good deals in options prices might be difficult to arbitrage away and why speculative investors do not compete with market-makers to provide liquidity by taking the short side of the trade in index options. The literature on limits to arbitrage has not reached complete consensus. While Battalio and Stultz (2006) find no evidence in favor of the limits to arbitrage argument, Ofek et al. (2004), Duarte et al. (2006), and Han (2008) find that relative mis-pricings are stronger when there are more impediments to arbitrage activity. Our paper adds to the above studies in providing further empirical evidence in favor of the limits to arbitrage argument. Under the opposite view that put option prices are perfectly consistent with large risk premia for volatility and/or jump risk, our results are still interesting in that they document how options might not be effective instruments for risk sharing among investors. The rest of the paper is organized as follows. In Section 1 we describe the data. We explain the option strategies studied in the paper and give summary statistics of the strategy returns in Section 2. Section 3 describes the margin requirements analyzed in this paper. In Section 4, we analyze the impact of margin requirements on the execution and the profitability of the strategies in the case where the investor is allowed to trade in options and the risk-free rate. We extend the investment opportunity set to include index futures in Section 5. Section 6 concludes.
1. Data
All our main tests are conducted using data provided by the Institute for Financial Markets for American options on S&P 500 futures traded at the CME. This dataset includes daily closing prices for options and futures traded between January 1985 and May 2001. We use data from OptionMetrics for European options on the S&P 500 index, which are traded at the CBOE to estimate bid–ask spreads for various levels of moneyness. This dataset includes daily closing bid and ask quotes for the period between January 1996 and April 2006.
4Few studies consider margin requirements in options: Heath and Jarrow (1987) show that the Black–Scholes model still holds. Mayhew et al. (1995) and John et al. (2003) study the implication of margins for liquidity and the speed at which information is incorporated into prices. Driessen and Maenhout (2007) and Driessen et al. (2008) incorporate margins in portfolio optimization exercises. There is also a vast literature that studies trading costs in the context of option markets. Some examples are Leland (1985), Figlewski (1989), Bensaid et al. (1992), Green and Figlewski (1999), Constantinides and Zariphopoulou (2001), Constantinides and Perrakis (2002), and Constantinides et al. (2008). ARTICLE IN PRESS P. Santa-Clara, A. Saretto / Journal of Financial Markets 12 (2009) 391–417 395
To minimize the impact of recording errors and to guarantee homogeneity in the data, we apply a series of filters. First, we eliminate prices that violate basic arbitrage bounds. Second, we eliminate all observations for which the bid is equal to zero, or for which the spread is lower than the minimum ticksize (equal to $0.05 for options trading below $3 and $0.10 in any other cases). Finally, we exclude all observations for which the implied Black (1976) volatility is larger than 200% or lower than 1%. We construct the option return from the closing of the first trading day of each month to the closing price of the first trading day of the next month. We obtain a time-series by computing the option return in each month of the sample. The returns of the strategies are not affected by the American nature of the options traded in the CME. We compute returns based on the prices published by the exchange that already include the early exercise premium assessed by the market participants. The results we obtain with the European options traded in the CBOE are very similar to the results obtained with the American options traded on the CME.
2. Option strategies
We analyze several option strategies standardized at different moneyness levels. We focus on one maturity, corresponding to approximately 45 days, and three different levels of moneyness, at-the-money (ATM), 5%, and 10% OTM. All the strategies are constructed so that they involve writing options. We consider only strategies that involve at least one put contract since those strategies have been found to generate large returns—see, for example, Coval and Shumway (2001), Bakshi and Kapadia (2003), Bondarenko (2003), Jones (2006), and Driessen and Maenhout (2007). We consider naked and covered positions in put options, delta-hedged puts, and combinations of calls and puts, such as straddles and strangles.5 A naked position is formed simply by writing the option contract. A covered put combines a negative position in the option and a short in the underlying. A delta-hedged put is formed by selling one put contract, as well as delta shares of the underlying. We also study strategies that involve combinations of calls and puts, such as straddles and strangles. A straddle involves writing a call and a put option with the same strike and expiration date. A strangle differs from a straddle in that the strike prices are different: write a put with a low strike and a call with a high strike.
2.1. Summary statistics
We start by discussing the characteristics of the options used in constructing the monthly returns. In Table 1, for any moneyness level, we tabulate the average Black and Scholes implied volatility and the average price as a percentage of the value of the underlying. This last information is essential to understand the magnitude of the portfolio weights that we will analyze in the following sections and gives us an idea of how expensive the options are relative to the underlying value. We report results for the S&P 500 futures options (CME sample) in Panel A and results for the S&P 500 index options (CBOE sample) in Panel B.
5In a previous version of this paper, we used to study a much wider set of option strategies. Although the result about these strategies are still interesting, we do not report them for the sake of brevity. These results are available from the authors upon request. ARTICLE IN PRESS 396 P. Santa-Clara, A. Saretto / Journal of Financial Markets 12 (2009) 391–417
Table 1 Descriptive statistics of option data.
Put Call
10% 5% ATM ATM 5% 10%
Panel A: CME sample 1985–2001 IV 0.254 0.224 0.192 0.186 0.173 0.161 Price/S 0.006 0.013 0.028 0.027 0.009 0.002
Panel B: CBOE sample 1996–2006 IV 0.264 0.229 0.198 0.196 0.175 0.169 Price/S 0.006 0.013 0.027 0.028 0.009 0.002
In this table we report the average Black and Scholes implied volatility (IV) as well as the average ratio of the option price to the value of the underlying index (price/S) for calls and puts on the S&P 500 futures. We focus on one maturity, corresponding to approximately 45 days to maturity. We report statistics for option at the money (ATM), and out-of-the-money by 5% and 10%. Option and S&P 500 future closing prices were sampled daily between January 1985 and May 2001. The data are provided by the Chicago Mercantile Exchange through the Institute for Financial Markets (all options are American). Options and S&P 500 index closing prices were sampled daily between January 1996 and April 2006. The data are provided by Optionmetrics (all options are European).
Table 2 Returns of option strategies.
Mean Std Min. Max. Skew. Kurt. SR LEL
Put ATM 0.296 0.861 0.990 5.249 2.680 13.049 0.344 0.152 Put 5% OTM 0.456 1.060 0.991 10.004 5.923 51.711 0.430 0.293 Put 10% OTM 0.509 1.663 0.990 20.628 10.880 136.358 0.306 0.308 Cov Put ATM 0.004 0.024 0.073 0.095 0.818 4.772 0.135 0.003 Cov Put 5% OTM 0.002 0.033 0.098 0.108 0.228 3.324 0.033 0.003 Cov Put 10% OTM 0.000 0.038 0.113 0.115 0.130 3.406 0.003 0.003 Delta Put ATM 0.011 0.029 0.063 0.233 3.894 29.712 0.376 0.001 Delta Put 5% OTM 0.018 0.047 0.092 0.469 6.557 64.081 0.377 0.007 Delta Put 10% OTM 0.020 0.085 0.130 1.084 11.261 145.891 0.236 0.012
Straddle ATM 0.117 0.474 0.970 2.845 2.531 12.571 0.247 0.088 Strangle 5% OTM 0.338 0.760 1.007 3.942 3.101 14.253 0.445 0.305 Strangle 10% OTM 0.510 0.779 1.007 5.676 4.484 29.156 0.654 0.496
This table reports summary statistics of the strategy returns: average, standard deviation, minimum, maximum, skewness, kurtosis, Sharpe ratio (SR), and Leland’s alpha (LEL). The returns are computed as the return to a strategy that writes the options. Options and S&P 500 futures closing prices were sampled daily between January 1985 and May 2001. The data are provided by the Chicago Mercantile Exchange through the Institute for Financial Markets. All options are American. For comparison, the S&P 500 index has a mean return of 1.3%, a standard deviation of 4.3%, skewness of 0.804, Sharpe ratio of 0.189, and Leland’s alpha of 0.
The average ATM implied volatility is around 19% in the 1985–2001 sample and around 20% in the 1996–2006 sample. In general, downside protection (OTM puts) is more expensive than upside leverage (OTM calls). Table 2 reports the average, standard deviation, minimum, maximum, skewness, kurtosis, Sharpe ratio, and Leland (1999) alpha of the monthly returns of the strategies ARTICLE IN PRESS P. Santa-Clara, A. Saretto / Journal of Financial Markets 12 (2009) 391–417 397 discussed in the previous section.6 As a first attempt, to understand the statistical properties of the strategies, we compute the return of a long position in the option, which is financed by borrowing at the risk-free rate. Table 2 is divided into four panels that group strategies with similar characteristics. The average returns of all the strategies are negative across all moneyness levels. Selling 10% OTM put contracts earns 51% per month on average, with a Sharpe ratio of 0.306, and a Leland alpha of 30% (first panel of Table 2). The reward is accompanied by considerable risk: the strategy has a negative skewness of –10.880, caused by a maximum possible loss of 20 times the notional capital of the strategy. These numbers are comparable to those reported by Bondarenko (2003). Protective put strategies also have negative returns; however, the Sharpe ratios are very small. Similarly to Bakshi and Kapadia (2003), we find that the delta-hedged returns are all associated with large Sharpe ratios (e.g., the 10% OTM delta-hedged put has an average return of 2:0% per month with a Sharpe ration of 0:236). The Leland alpha, however, is positive at 1.2%, indicating that, according to that performance measure, writing delta-hedge puts would not be a good investment. Straddles and strangles offer high average returns, Sharpe ratios, and Leland alphas, which are increasing with the level of moneyness: a short position in the ATM straddle returns on average 11% per month, with a Sharpe ratio of 0.247 and a Leland alpha of 8.8%, while a short position in the 10% OTM strangle earns an average 51% per month, with a Sharpe ratio of 0.654 and a Leland alpha of 49%. These numbers are comparable to those reported by Coval and Shumway (2001). Similar statistics for the European S&P 500 index options, over the period 1996–2006, can be found in the first three columns of Table 4. In that sample, the average strategy returns are very close to the average returns in the 1985–2001 sample. However, the strategy volatilities are lower in the 1996–2006 sample, thus leading to higher Sharpe ratios. Although the general performance of the strategies is consistent in various sub-samples, the inclusion of the October 1987 crash does change the magnitude of the profitability of some strategies. For this reason, we prefer to leave the pre-crash observations in the sample despite the evidence that a structural break did occur in those years (for example, Jackwerth and Rubistein, 1996; Benzoni et al., 2005), and the fact that the maturity structure of the available contracts changed after the crash (for example, Bondarenko, 2003). Complete summary statistics for the various sub-samples are not reported in the paper. A brief discussion follows. Let us consider, for example, the 5% OTM put. The average return for the years around the 1987 market crash, January 1985 to December 1988, is 25:2%, while in the rest of the sample, January 1989 to May 2001, the strategy averages 52:1%. Even if we consider the more recent period that starts with the burst of the ‘‘Internet bubble,’’ 2001 up to 2006, the return of the S&P 500 index put still averaged 30% per month in a substantially bearish market.
6Leland (1999) provides a simple correction of the CAPM, which allows the computation of a robust risk measure for assets with arbitrary return distributions. This measure is based on the model proposed by Rubinstein (1976) in which a CRRA investor holds the market in equilibrium. The discount factor for this economy is the marginal utility of the investor and expected returns have a linear representation in the beta derived by Leland. Subtracting Leland’s beta times the market excess return from the strategy returns gives an estimate of the strategy alpha. Results for the alpha derived from CAPM and the Fama and French (1993) three factor model are very similar and are available from the authors upon request. ARTICLE IN PRESS 398 P. Santa-Clara, A. Saretto / Journal of Financial Markets 12 (2009) 391–417
2.2. Statistical significance
Inference on the statistics reported in Table 2 is particularly difficult since the distribution of option returns is far from normal, and characterized by heavy tails and considerable skewness. For this reason, the usual asymptotic standard errors are not suitable for inference. Instead, we base our tests on the empirical distribution of returns obtained from 1000 non-parametric bootstrap repetitions of our sample. Each repetition is obtained by drawing with replacement the returns of the strategies. We construct and report the 95% confidence interval or the p-value under the null hypothesis. An exact description of the bootstrap procedure can be found in Davison and Hinkley (1997). In Table 3, we present 95% confidence intervals for the mean, Sharpe ratio, and Leland alpha of the different strategies. We note that 9 out of 12 strategies have mean returns, Sharpe ratio and Leland alphas are statistically different from zero at the 5% level. None of the covered puts has statistically significant means or Sharpe ratios or Lelans’s alphas. Four strategies have Sharpe ratios that are statistically higher than the market’s Sharpe ratio at the 95% confidence level: the 5% OTM put, the ATM Delta-Hedge Put, and the 5% and 10% OTM strangles. In general, however, Sharpe ratios and Leland alphas are really large, especially for strategies that are not very correlated with the market.
2.3. Transaction costs
Trading options can be quite expensive, not only because of the high commissions charged by brokers, but, most importantly, because of the large bid–ask spreads at which options are quoted. We investigate the magnitude of bid–ask spreads, as well as their
Table 3 Bootstrapped confidence intervals.
Mean (95%) SR (95%) LEL (95%)
Put ATM 0.404 0.176 0.605 0.175 0.407 0.164 Put 5% OTM 0.583 0.304 0.948 0.204 0.593 0.293 Put 10% OTM 0.682 0.249 1.332 0.092 0.699 0.241 Cov Put ATM 0.006 0.000 0.296 0.002 0.002 0.005 Cov Put 5% OTM 0.006 0.003 0.177 0.101 0.003 0.004 Cov Put 10% OTM 0.005 0.005 0.142 0.135 0.006 0.009 Delta Put ATM 0.015 0.007 0.705 0.189 0.009 0.003 Delta Put 5% OTM 0.023 0.011 0.916 0.157 0.012 0.003 Delta Put 10% OTM 0.029 0.007 1.066 0.051 0.014 0.003 Straddle ATM 0.188 0.057 0.493 0.104 0.183 0.051 Strangle 5% OTM 0.446 0.242 0.810 0.268 0.442 0.234 Strangle 10% OTM 0.614 0.399 1.294 0.388 0.617 0.402
This table reports 95% bootstrap confidence intervals for three of the summary statistics reported in Table 2: average return, Sharpe ratio, and Leland’s alpha. The empirical distribution of returns is obtained from 1000 non- parametric bootstrap repetitions of our sample. Each repetition is obtained by drawing with replacement the returns of the strategies. Options and S&P 500 futures closing prices were sampled daily between January 1985 and May 2001. The data are provided by the Chicago Mercantile Exchange through the Institute for Financial Markets. All options are American. ARTICLE IN PRESS P. Santa-Clara, A. Saretto / Journal of Financial Markets 12 (2009) 391–417 399
Table 4 Impact of transaction costs on option strategies’ returns.
Mid-price Bid-to-ask
Mean SR LEL Mean SR LEL
Put ATM 0.251 0.307 0.186 0.197 0.229 0.129 Put 5% OTM 0.463 0.599 0.406 0.401 0.486 0.340 Put 10% OTM 0.612 1.054 0.572 0.521 0.801 0.476
Delta Put ATM 0.011 0.673 0.011 0.008 0.508 0.008 Delta Put 5% OTM 0.017 0.748 0.018 0.014 0.600 0.014 Delta Put 10% OTM 0.023 0.907 0.025 0.018 0.714 0.020 Straddle ATM 0.181 0.666 0.187 0.128 0.460 0.135 Strangle 5% OTM 0.352 0.673 0.350 0.276 0.497 0.274 Strangle 10% OTM 0.519 0.972 0.510 0.400 0.666 0.388
In this table we analyze the impact of the bid-ask spread on the strategies’ returns. For each strategy, we report the mean return, the Sharpe ratio, and the Leland alpha under two scenarios: trades executed at mid-point prices (left part of the table) and trades executed at the bid price when options are written and at the ask price when options are bought (right part of the table). Options and S&P 500 index closing prices were sampled daily between January 1996 and April 2006. The data are provided by Optionmetrics. All options are European. impact on strategy returns by analyzing the S&P 500 index option OptionMetrics database, which provides the best closing bid and ask prices of every trading day. This database covers a shorter and more recent period (January 1996 to April 2006) than the futures option database that was used in the previous section. Therefore, the trading costs that we estimate are, if anything, lower than those prevailing in the first part of the longer sample. In Table 4, we compare average, Sharpe ratio, and Leland alpha of the strategy returns obtained with and without accounting for transaction costs. We compute the relevant return for an investor writing options from mid-price to mid-price (left part of the table) and from bid to ask price (right part of the table). The comparison of the statistics in the two scenarios confirms the findings of George and Longstaff (1993). Average returns from writing puts are 5%–9% per month lower when transaction costs are considered.7 The return difference is larger for OTM options than it is for ATM options. The impact of trading costs on the return of straddles and strangles is similar. For example, the bid-ask spread accounts for a loss of 5.3% for the ATM straddle. The impact on delta-hedged strategies is lower in absolute terms but it is approximately of the same proportional magnitude. Transaction costs decrease Sharpe ratios by even larger proportions, due to the fact that the strategy volatility is also affected. The impact of transaction costs on Leland alphas is very similar in magnitude to the impact on average returns. As we were expecting given the extensive literature on the topic (see, for example, Constantinides et al., 2008) transaction costs do not completely eliminate the profitability of the option strategies. The impact is, however, economically important, making the inclusion of round-trip costs essential for the rest of our analysis.
7If the investor holds the options to maturity, only half of the cost is incurred. ARTICLE IN PRESS 400 P. Santa-Clara, A. Saretto / Journal of Financial Markets 12 (2009) 391–417
The evidence presented in this section, which essentially confirms the findings already reported in the vast existing literature, establishes that several strategies involving writing options have produced large average returns (even after transaction costs). Many attempts to directly or indirectly explain this empirical regularity have been proposed: remuneration for volatility and jump risk, demand pressure, non-standard preferences, and market segmentation (see Bates, 2003 for a review). All these factors have an impact on how options are priced and might, therefore, be responsible for the ‘‘high’’ put prices that generate the profitability of the option strategies. It is not clear however what portion of these profits is attributable to remuneration for risk (see, for example, Jones, 2006). We conjecture that returns to option trading strategies are affected by market frictions, creating a wedge between the returns that are observable and those that are realizable. In the following sections, we investigate the feasibility of these option strategies, focusing in particular on how margin requirements impact the returns of the strategies.
3. Margin requirements
All the strategies studied in this paper involve a short position in one or more put contracts. When an investor writes an option, the broker requests a deposit in a margin account of cash or cash-equivalent instruments such as T-bills. The amount requested corresponds to the initial margin requirement. The initial margin is the minimum requirement for the time during which that position remains open. Every day a maintenance margin is also calculated. A margin call originates only if the maintenance margin is higher than the initial margin. If the investor is unable to provide the funds to cover the margin call, the option position is closed and the account is liquidated. Minimum margin requirements are determined by the option exchanges under supervision of the Security Exchange Commission (SEC) and the Commodity Futures Trading Commission (CFTC). Margin keeping is maintained by members of clearing houses.8 There are essentially three types of account that are maintained by members of a clearing house: market-maker accounts, proprietary accounts, and customer accounts. The difference among these accounts is that market-maker accounts are margined on their net positions (short positions can be offset by long positions) while other accounts are margined on all the existing short positions. In this paper, we study the customer minimum margin requirements imposed by the CBOE, and the proprietary (speculative) account margins imposed by the CME to its members. The margin requirements that are applied by the two clearing houses to members are very similar in their spirit. The CME has a system called Standard Portfolio Analysis of Risk (SPAN), while the OCC has a system called Theoretical Intermarket Margin System (TIMS). Both systems are based on scenario analysis, and in what follows we assume them to be interchangeable.9 Moreover, some
8In the United States there are 11 Derivatives Clearing Organizations registered with the CFTC. Of these, the CME clears trades on futures and futures options traded at the CME, while the Options Clearing Corporation (OCC) clears trades on the stock and index options traded at the American Stock Exchange, the Boston Options Exchange, the CBOE, the International Securities Exchange, the Pacific Stock Exchange, and the Philadelphia Stock Exchange. 9The OCC does not have any available technical documentation that could be used to reconstruct the exact functioning of the TIMS system. However, conversation with OCC personnel confirmed that the system is similar to SPAN. ARTICLE IN PRESS P. Santa-Clara, A. Saretto / Journal of Financial Markets 12 (2009) 391–417 401 large institutional players, which are not members of a clearing house, have special arrangements (often through off-shore accounts) to essentially get the same terms as clearing house members. Therefore, the analysis of the margins on customer accounts (retail investors) and on brokers’ proprietary accounts should be sufficient to uncover the impact of the margining system on the key players in the option market.
3.1. The CBOE minimum margins for customer accounts
The margin requirements for customers depend on the type of option strategy and on whether the short positions are covered by a matching position in the underlying asset. The margin for a naked position is determined on the basis of the option sale proceeds, plus a percentage of the value of the underlying asset, less the dollar amount by which the contract is OTM, if any.10 Specifically, for a naked position in a call or put option, the margin requirement at time t can be found by applying the following simple rules: